# Properties

 Label 6930.v Number of curves $2$ Conductor $6930$ CM no Rank $1$ Graph

# Learn more

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 6930.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.v1 6930s1 $$[1, -1, 1, -233, 1321]$$ $$51603494067/4336640$$ $$117089280$$ $$[2]$$ $$2560$$ $$0.28997$$ $$\Gamma_0(N)$$-optimal
6930.v2 6930s2 $$[1, -1, 1, 247, 5737]$$ $$61958108493/573927200$$ $$-15496034400$$ $$[2]$$ $$5120$$ $$0.63655$$

## Rank

sage: E.rank()

The elliptic curves in class 6930.v have rank $$1$$.

## Complex multiplication

The elliptic curves in class 6930.v do not have complex multiplication.

## Modular form6930.2.a.v

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} + q^{11} + 2 q^{13} - q^{14} + q^{16} - 2 q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.